A345723 Numbers that are the sum of six fifth powers in nine or more ways.

9085584992, 16933805856, 37377003050, 39254220544, 41066625600, 41485873792, 42149876800, 43828403850, 44180505600, 45902654525, 48588434400, 52005184992, 53536896864, 54156285568, 55302546200, 56229189632, 57088402525, 59954496800, 63432407850

Offset: 1

Author

David Consiglio, Jr., Jun 24 2021

Keywords

• nonn

Examples

			16933805856 =  2^5 + 38^5 + 68^5 + 74^5 + 92^5 +  92^5
            =  2^5 + 54^5 + 58^5 + 64^5 + 92^5 +  96^5
            = 14^5 + 36^5 + 61^5 + 67^5 + 94^5 +  94^5
            = 15^5 + 49^5 + 52^5 + 60^5 + 94^5 +  96^5
            = 17^5 + 49^5 + 53^5 + 57^5 + 92^5 +  98^5
            = 29^5 + 36^5 + 42^5 + 72^5 + 88^5 +  99^5
            = 31^5 + 36^5 + 54^5 + 54^5 + 94^5 +  97^5
            = 34^5 + 34^5 + 46^5 + 72^5 + 76^5 + 104^5
            = 35^5 + 36^5 + 69^5 + 72^5 + 89^5 +  95^5
so 16933805856 is a term.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..127

Crossrefs

Cf. A344196, A345566, A345631, A345722, A346364.

Programs

Python

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 9])
    for x in range(len(rets)):
        print(rets[x])